Logarithmic singularities of solutions to nonlinear partial differential equations

TAHARA, Hidetoshi; YAMANE, Hideshi

J. Math. Soc. Japan, Tome 60 (2008) no. 1, p. 603-630 / Harvested from Project Euclid

Résumé

We construct a family of singular solutions to some nonlinear partial differential equations which have resonances in the sense of a paper due to T.Kobayashi. The leading term of a solution in our family contains a logarithm, possibly multiplied by a monomial. As an application, we study nonlinear wave equations with quadratic nonlinearities. The proof is done by the reduction to a Fuchsian equation with singular coefficients.

Publié le : 2008-04-15
Classification: singular solutions, Fuchsian equations, logarithmic singularities, nonlinear wave equations, 35A20, 35L70

@article{1212156664,
     author = {TAHARA, Hidetoshi and YAMANE, Hideshi},
     title = {Logarithmic singularities of solutions to nonlinear partial differential equations},
     journal = {J. Math. Soc. Japan},
     volume = {60},
     number = {1},
     year = {2008},
     pages = { 603-630},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1212156664}
}

TAHARA, Hidetoshi; YAMANE, Hideshi. Logarithmic singularities of solutions to nonlinear partial differential equations. J. Math. Soc. Japan, Tome 60 (2008) no. 1, pp.  603-630. http://gdmltest.u-ga.fr/item/1212156664/